Encryption and HUGE numbers - Numberphile

Banks, Facebook, Twitter and Google use epic numbers - based on prime factors - to keep our Internet secrets. This is RSA public-key encryption.
More links & stuff in full description below ↓↓↓

Regarding the keys used for encryption:
x, y prime
Encode key E shares no factors with (x-1)(y-1)
Decode key is D with E*D - 1 a multiple of (x-1)(y-1)

NUMBERPHILE

Videos by Brady Haran

[autohmae]

I've been in IT for more than 15 years, I've never seen a analogy as good as yours for public key encryption. Thanks for that padlock analogy, now it will be much easier for me to explain to people.

[clickrick]

"...so they lock it with a padlock, and you can't open it up."
*over on another channel...*
"This is the LockPickingLawyer, and what I have for you today is a padlock..."

[shawn]

What is this nonsense? I just use the password "12345" for everything.

[piguy]

How to get the "secret" number:
Let P and Q be the two primes that make the "big" number, and let X = (P - 1)(Q - 1). The secret number is the smallest positive integer S such that if you multiply S by the "small" number and subtract 1, you get a multiple of X.

In the example, P = 2 and Q = 5, so X = (2 - 1)(5 - 1) = 1 * 4 = 4. Thus, we want 3*S - 1 to be a multiple of 4. The smallest S where this works is S = 3: 3*3 - 1 = 8. Hence, the secret number is 3.

Note: For this to work, the "small" number must not share any factors (other than 1) with X.

[matthewclifford]

I'm a horrible Math student. However there is a weird problem that I like these kinds of videos better than lectures in class.

[harvyhun]

"1024 could be broken in a few years"
Me watchin in 2019....

[numberphile]

cheers Drew - this was great! Just what we needed!

[GaussTruth]

@ 4:10
"there is a formula to work out the secret number, I'm going to gloss over that for a second"

So, how to you work out the secret number?
 

[Gunbudder]

I LOVE that Drewmo did the animation for this. I love seeing his work pop up randomly over the years. he is an awesome guy and i've been a super fan for a very long time lol

[andriyshevchenko]

This kind of encryption is used in HTTPS (or better, SSL) but it doesn't make a site that uses a longer key inherently safer. HTTPS is essentially only there to make sure some guy on your wifi network can't intercept your traffic, but it does nothing to protect against bugs on the actual site which are far easier to exploit and are just as effective

[jomiar]

I really enjoy these videos, where you take something that seems abstract, and show what it's really used for! Can you do a video (or maybe a series of videos) on Fourier transforms, and their use in computing?

[blackmadra]

Why did you use 3 twice? It made it very difficult to follow!

[therealfreeman]

I love the passion for mathematics that is conveyed through this video :)

[numberphile]

the piece of paper in this video is currently on ebay - see link in full video description

[artisticcheese]

Would you please make a video about elleptical curves algorythms in comparison to RSA based in public cryptography

[DustinScherer]

I'm digging the animated format of this one! Good work Brady!

[nerhu]

Google just announced updates to their security of gmail, does anyone know if that means they bumped it to 2048 bit?

[RoSiYou]

I am not into math at all, but I am able to listen to You for hours!

[ericeinarson]

I'm very confused. He said that the numbers 3 and 10 were publicly available- anyone can see them. But he then said the key to braking the code, depends on determining the primes that were multiplied together to create that number... How? How does knowing 5 and 2 help? Can someone please explain?

[StepSkatin]

Yes pleaseeee. I'm a computer science major and your videos just drive my engines up to create monumentally powerful code! Thank you!!!